A review on swing-up methods in inverted pendulums

Inverted pendulum systems are considered a fundamental criterion in comparing and validating control methods due to their nonlinear, unstable, and underactuated nature. In this study, swing-up methods that raise the inverted pendulum from a hanging position to a vertical position are comprehensively examined in light of the literature. Linear and rotary inverted pendulum systems are presented along with their mathematical models, and inverted pendulum swing-up methods found in the literature are presented along with the studies conducted,, the methods used to keep the inverted pendulum in equilibrium are listed, and inverted pendulum swing-up methods found in the literature are presented along with the studies conducted. The methods used are evaluated starting from their first proposed studies and including their current applications. In this context, the new roles of classical energy-based methods in soft robotics applications are discussed; the Hedge Algebra approach, which optimizes the computational load in fuzzy logic-based systems, is examined. In addition, the success of Deep Reinforcement Learning algorithms, which offer model-independent control, especially in overcoming "Sim-to-Real" challenges, is discussed through current publications. This review provides a broad perspective, ranging from traditional control approaches to AI-driven learning systems, offering a current and comprehensive roadmap for researchers.